It is known that a nondeterministic input-driven pushdown automaton (IDPDA) can be determinized. Alur and Madhusudan (Adding nesting structure to words, J.ACM 56(3), 2009) showed that a deterministic IDPDA simulating a nondeterministic IDPDA with n states and stack symbols may need, in the worst case, states. In their construction, the equivalent deterministic IDPDA does, in fact, not need to use the stack. This paper considers the size blow-up of determinization in more detail, and gives a lower bound construction, that is tight within a multiplicative constant, with respect to the size of the nondeterministic automaton both for the number of states and the number of stack symbols. The paper also surveys the recent results on operational state complexity of IDPDAs, and on the cost of converting a nondeterministic automaton to an unambiguous one, and an unambiguous automaton to a deterministic one.